Space of modular forms of level 54, weight 4, and Character 54.e

• Label: 54.4.e
• Level: $54$
• Weight: $4$
• Character orbit: 54.e
• Rep. character: $\chi_{54}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $54$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(54, [\chi])\).

	Total	New	Old
Modular forms	174	54	120
Cusp forms	150	54	96
Eisenstein series	24	0	24

Trace form

\( 54 q - 24 q^{5} + 12 q^{6} + 24 q^{8} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(54, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
54.4.e.a	$54$	$4$	54.e	27.e	$9$	$24$	$4$	$3.186$		None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-33\)		$\mathrm{SU}(2)[C_{9}]$
54.4.e.b	$54$	$4$	54.e	27.e	$9$	$30$	$5$	$3.186$		None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(33\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{4}^{\mathrm{old}}(54, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(54, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)